On homotopy invariants of maps to the circle
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 187-202
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Homotopy classes of maps of a space $X$ to the circle $T$ form an Abelian group $B(X)$ (Bruschlinsky group). A map $f\colon B(X)\to C$, where $C$ is an Abelian group, has order at most $r$ if for a continuous map $a\colon X\to T$ the value $f([a])$ can be $\mathbb Z$-linearly expressed in terms of the indicator function $I_r(a)\colon(X\times T)^r\to\mathbb Z$ of the $r$th Cartesian power of the graph of $a$. We prove that the order of $f$ equals the algebraic degree of $f$. (A map between abelian groups has degree at most $r$ if its finite differences of order $r+1$ vanish.) Bibl. – 2 titles.
@article{ZNSL_2009_372_a17,
author = {S. S. Podkorytov},
title = {On homotopy invariants of maps to the circle},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {187--202},
year = {2009},
volume = {372},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a17/}
}
S. S. Podkorytov. On homotopy invariants of maps to the circle. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 187-202. http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a17/